1. Field of the Invention
The present invention relates to signal processing and more particularly relates to took-ahead delta-sigma modulators with time weighted error values.
2. Description of the Related Art
Many signal processing systems implement look-ahead delta-sigma modulators in an attempt to obtain superior input/output signal fidelity by minimizing quantization error. “Delta-sigma modulators” are also commonly referred to using other interchangeable terms such as “sigma-delta modulators”, “delta-sigma converters”, “sigma delta converters”, and “noise shapers”. FIG. 1 depicts a prior art signal processing system 100 having a look-ahead delta-sigma modulator 102. Table 1 describes the symbols used in FIG. 1.
TABLE 1SymbolDefinitionx(n)The nth discrete input signal.XtInput signal vector at a time t.y(n)The nth discrete output signal.YiThe ith output candidate vector.Di(z)The ith difference vector = Xt − Yi.CiThe ith cost value vector = H(Di(z)).MLook-ahead depth.NN = kM = The number of outputsignal candidate sets underconsideration, and k = number ofpossible values for y(n).ii is selected from the set {0, 1, 2, . . .N − 1}.C(2)iThe ith cost value power.C(2)minThe minimum cost value power attime t.
The signal source 102 provides an input signal to pre-processing components 104. Preprocessing components include an analog-to-digital converter (“ADC”) and oversampling components to generate a k-bit, digital input signal x(n). For audio applications, x(n) represents a 44.1 kHz signal with a desired oversampling ratio. Look-ahead modulator 106 quantizes input signal x(n) and shapes the quantization noise so that most of the quantization noise is moved out of the signal band of interest, e.g. approximately 20 kHz for audio applications. Each output signal y(n) generally has one of two values selected from the set {+Δ/2, −Δ/2} with “Δ” representing the full swing of y(n). (For convenience, Δ/2 will be represented as +1, and −Δ/2 will be represented as −1.). The output signal y(n) can be processed further and, for example, used to drive an audio sound system or can be recorded directly onto a storage medium.
FIG. 2 depicts a schematic representation of prior art look-ahead delta-sigma modulator 106 with a look-ahead depth of M. The look-ahead depth refers to the dimension of each output candidate vector Yi used to determine output signal y(n). For time t, each output candidate vector Yi, i□{0,1,2, . . . , N−1}, is subtracted from an input vector Xt to obtain respective difference vectors Di, i□{0,1,2, . . . , N−1}, and Di=[Xt-Yi]. For a look-ahead depth of M and y(n)={−1, +1}, and without pruning output candidates, each of the N output candidate vectors contains a unique set of elements. Each noise-shaping filter 202(i) of look-ahead delta-sigma modulator 106 uses a common set of filter state variables for time t during the calculations of respective cost vectors Ci. Filter 202 maintains the actual filter state variables used during the calculation of each y(n). The state variables are updated with the selected y(n) output value. The output of each filter 202(i) is a cost value vector, Ci. Cost value vector Ci=H(Di(z)), and, thus, each element of cost value vector Ci is a frequency weighted error value.
Quantizer 203 includes two modules to determine y(n). The cost function minimum search module 204 computes the cost value power, Ci(2), of each cost value Ci in accordance with Equation 1, and determines the minimum cost value power at time t.                               C          i                      (            2            )                          =                              ∑                          t              =              1                                      t              =              M                                ⁢                                           ⁢                                                    [                                  c                  t                                ]                            2                        .                                              Equation        ⁢                                   ⁢        1            “ct” represents a cost value for time t, t=1 through M, in the cost vector Ci.
The y(n) selector module 206 selects y(n) as the leading bit of Yi where Ci(2)min represents the minimum cost value power.
For example, if M=2 and yε{−1,+1}, then N=4, i□{0,1,2,3}, and Table 2 represents each of the Y output candidate vectors and Xt.
TABLE 2Y1Y2Y3Y4Xtyt0011x(n)yt+10101x(n + 1)
If C3(2) represents the minimum cost value power, then selector module 206 selects y(n)=1 because the first bit in output candidate vector Y3 (the output candidate vector associated with C3(2)), equals 1. If C1(2) represents the minimum cost value power, then selector module 206 selects y(n)=0 because the first bit in output candidate vector Y1 (the output candidate vector associated with C1(2)), equals 0.
Conventional research in look-ahead modulators primarily involves two threads. The first are the works of Hiroshi Kato, “Trellis Noise-Shaping Converters and 1-bit Digital Audio,” AES 112th Convention, 2002 May 10-13 Munich, and Hiroshi Kato, Japanese Patent JP,2003-124812,A, and further refinements described in Harpe, P., Reefman D., Janssen E., “Efficient Trellis-type Sigma Delta Modulator,” AES 114th Convention, 2003 Mar. 22-25 Amsterdam (referred to herein as “Harpe”); James A. S. Angus, “Tree Based Look-ahead Sigma Delta Modulators,” AES 114th Convention, 2003 Mar. 22-25 Amsterdam; James A. S. Angus, “Efficient Algorithms for Look-Ahead Sigma-Delta Modulators,” AES 155th Convention, 2003 Oct. 10-13 New York; Janssen E., Reefman D., “Advances in Trellis based SDM structures,” AES 115th Convention, 2003 Oct. 10-13 New York. This research targets solving the problems of 1-bit encoding of audio data for storage without using the steep anti-alias filters associated with pulse code modulation “PCM.” The advent of super audio compact disc “SACD” audio storage, with its moderate oversample ratios (32 or 64), motivated this work.
The second primary thread of look-ahead modulator research involves pulse width modulation (“PWM”) amplifiers based on delta-sigma modulators combined with digital PWM modulation stages. The principal researchers have been Peter Craven and John L. Melanson. In U.S. Pat. No. 5,784,017 entitled “Analogue and Digital Converters Using Pulse Edge Modulations with Non-Linear Correction,” inventor Peter Craven (“Craven”), which is incorporated herein by reference in its entirety, Craven described the use of look-ahead in delta sigma modulators. The purpose of Craven was to ensure stability in alternating edge modulation, an inherently difficult modulation mode to stabilize. In the PWM case, the delta-sigma modulator is operating at a low oversample ratio (typically 4-16), and quantization noise is a special problem.
Conventional technology has not proposed a reasonable way to find the closest matching output signal sets for each time t directly given that without pruning there are 2M possible reasonable combinations to search and the length of output signals Y[n] for a 1 minute signal is 60*44100*64 (i.e., 60 seconds, 44.1 kHz sampling frequency, and 64:1 oversample ratio). Trellis searches, tree searches, and pruning have all been proposed as solutions to reducing the computation.
As discussed in Harpe, page 5, conventional look-ahead delta-sigma modulators demonstrate improved linearity over standard (non-look-ahead) delta-sigma modulators. However, Harpe also observes on page 5 that in all cases the signal-to-noise ratio of Trellis architecture look-ahead delta-sigma modulators is several dB worse when compared to standard delta-sigma-modulators.